Big data are pervasively generated by human cognitive processes, formal inferences, and system quantifications. This paper presents the cognitive foundations of big data systems towards big data science. The key perceptual model of big data systems is the recursively typed hyperstructure (RTHS)....

We introduce a class of dynamical systems called Higher Order Cellular Automata (HOCA). These are based on ordinary CA, but have a hierarchical, or multi-level, structure and/or dynamics. We present a detailed formalism for HOCA and illustrate the concepts through four examples. Throughout the...